Method and apparatus for determining peripheral breast thickness

ABSTRACT

A method, computer software product and computer system for analyzing digital mammograms. The method, computer software product and computer system involve a generating phantom thickness object; receiving a set of dimensions for a breast; and, transforming the phantom thickness object to conform to the set of dimensions for the breast to provide the three-dimensional breast thickness object.

FIELD OF THE INVENTION

This invention relates in general to a method and apparatus fordetermining the thickness of a breast subjected to a mammogram, and morespecifically relates to a method and apparatus for determining thethickness of a breast at its peripheral portion.

BACKGROUND OF THE INVENTION

In conventional mammography, a woman places her breast on a breastsupport plate of the mammography machine. A detector is typicallymounted under the breast support plate. This detector is sensitive tox-rays. A breast compressor plate that is transparent to light andx-rays presses down against the top of the breast to flatten it and toprevent any movement of the breast during the mammogram. An x-ray sourceis then turned on to image the breast between the breast support plateand the breast compression plate.

Mammograms provide clues that help to distinguish benign and malignantbreast diseases. Radiologists look at both the static appearance of thebreast, as well as changes in its structure, micro-classification,density and other characteristics. Breast density determined from themammogram has been linked to increased link of breast cancer. Women withhigh mammographic densities (i.e., a high proportion ofradiographically-opaque stroma and parenchyma) have been shown to be atan increased risk of breast cancer, when compared to a woman whosebreasts are composed mainly of fatty or adipose tissue. Classificationof radiological appearance of mammograms on the basis of the generaldistribution of parenchyma, stroma and fat, can yield very strongestimates of breast cancer risk.

In the mammography field, various systems and methods have beendeveloped to quantify breast density in terms of the fraction of theprojected breast area that is occupied by radiographically dense tissue.These methods suffer from at least two limitations. First, they do notuse information about three-dimensional conformation of the breast. Asimple area measurement may provide an erroneous measure of the actualamount of fibroglandular tissue in the breast.

The computation of volumetric density in a compressed breast is based onboth image data and knowledge of the thickness at each pixel. However,at the breast periphery, where the breast is not bounded by either thebreast support plate or the breast compression plate, the thickness ofthe breast may not be known. However, this thickness is required todetermine volumetric density of the compressed breast.

Accordingly, a method and apparatus for determining the thickness of abreast at its periphery is desirable.

SUMMARY OF THE INVENTION

An object of one aspect of the present invention is to provide a methodof generating a three-dimensional breast thickness object for a digitalmammogram of a breast.

In accordance with one aspect of the present invention, there isprovided a method of generating a three-dimensional breast thicknessobject for a digital mammogram of a breast. The method comprises:

(a) generating a phantom thickness object for transforming into thebreast thickness object, the phantom thickness object being generated ina three-dimensional modeling means and being substantiallybreast-shaped;

(b) determining a set of dimensions for the breast; and

(c) transforming the phantom thickness object to conform to the set ofdimensions to provide the three-dimensional breast thickness object inthe three-dimensional modeling means.

An object of a second aspect of the present invention is to provide acomputer program product for use on a computer system for analyzingdigital mammograms.

In accordance with a second aspect of the present invention, there isprovided a computer program product for use on a computer system oranalyzing digital mammograms. The computer program product comprises:

(a) a recording medium;

(b) phantom thickness object generation means recorded on the recordingmedium for instructing the computer system to generate the phantomthickness object;

(c) data entry generation means recorded on the recording medium forinstructing the computer system to upload a set of dimensions for thebreast; and,

(d) transformation generation means recorded on the recording medium forinstructing the computer system to transform the phantom thicknessobject to conform to the set of dimensions for the breast to provide thethree-dimensional breast thickness object

An object of a third aspect of the present invention is to provide acomputer system for analyzing digital mammograms.

In accordance with a third aspect of the present invention, there isprovided a computer system for analyzing digital mammograms. Thecomputer system comprises:

(a) phantom thickness object generation means for generating the phantomthickness object;

(b) data entry means for receiving a set of dimensions for a breast;and,

(c) transformation means for transforming the phantom thickness objectto conform to the set of dimensions for the breast to provide thethree-dimensional breast thickness object.

BRIEF DESCRIPTION OF THE DRAWINGS

A detailed description of preferred aspects of the invention is providedherein below with reference to the following drawings, in which:

FIG. 1, in a perspective view, illustrates a mammography machine;

FIG. 2, in a sectional view, illustrates a breast phantom imageconstructed of poly-methyl-methacrylate (PMMA);

FIG. 3, in a perspective view, illustrates a three-dimensional trianglephantom image;

FIG. 4, in a schematic view, illustrates a breast compressed during amammogram;

FIG. 5 is a graph of polynomial conversion functions obtained from thethree-dimensional triangle phantom image of FIG. 3;

FIG. 6 is a graph of a grey value histogram of a digital mammogram;

FIG. 7 shows a phantom thickness map object;

FIG. 8 shows a digital mammogram object;

FIG. 9 illustrates the phantom thickness map object of FIG. 7 includinginternal and external sets of landmarks;

FIG. 10 illustrates the digital mammogram object of FIG. 8 includinginternal and external sets of landmarks;

FIG. 11 is a graph of a thickness profile for the phantom thickness mapobject of FIG. 7;

FIG. 12 is a graph illustrating a thickness profile of the digitalmammogram of FIG. 8;

FIG. 13 is a flowchart illustrating a method of generating a phantomthickness map in accordance with an aspect of the invention;

FIG. 14 is a flowchart illustrating a method of generating a breastthickness object in accordance with a preferred aspect of the invention;

FIG. 15 is a flowchart illustrating a method of generating phantomlandmarks for the phantom thickness map object of FIG. 13; and,

FIG. 16 is a flowchart illustrating a method of determining breastlandmarks of the breast thickness object in accordance with an aspect ofthe invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

Referring to FIG. 1, there is illustrated in a perspective view, amammography machine 12. The mammography machine 12 includes a breastsupport plate 14, a breast compression plate 18, and an x-ray tube 16.In operation, the x-ray tube 16 projects x-rays through the breastcompression plate 18, which is transparent to light and x-rays, throughthe breast, and through the breast support plate 14. The breastcompression plate 18 may be vertically adjusted to accommodate breastsof different dimensions. The breast support plate 14 includes a detector(shown in FIG. 4) that is sensitive to the x-rays. Variation in thedensity and thickness of the breast will affect the x-rays travelingthrough the breast. This in turn will affect the image left on thedetector in the breast support plate 14. These signal variations maythen be examined for possible malignancies or other conditions. However,to determine density, and thus to properly interpret the image, thethickness of the breast must be known at all points.

Referring to FIG. 4, a breast that is compressed between the breastsupport plate 14 and the breast compression plate 18 is shown in aschematic view. The breast 13 is of a thickness T in centimeters. X-raysoriginating from an x-ray tube 16 project through the breast compressionplate 18, any empty space surrounding the breast, the breast, and breastsupport plate 14 to impinge on a detector 20 underneath the breastsupport plate. When they impinge on the detector 20, the x-rays 15contain information about the thickness and composition of that portionof the breast through which they have passed. However, the x-rays willalso have been affected by the empty space between the breast supportplate 14 and breast compression plate 18 through which they have passed.At some points, of course, where the breast is in contact with both thebreast support plate 14 and breast compression plate 18, there will beno empty space. However, at other points, the curvature of the breastcreates a space between the breast compression plate 18 and the breastsupport plate 14 that is not occupied by the breast. If the thickness ofthe breast is known, then this information can be taken into accountwhen interpreting the x-ray data on the detector 20.

Referring to FIG. 7, there is illustrated a phantom thickness map object22 generated using three-dimensional modeling software in accordancewith an aspect of the present invention. This phantom thickness mapobject 22 is generated using a breast phantom 24 constructed ofpoly-methyl-methacrylate (PMMA) shown in FIG. 2. This phantom breast 24is first imaged by the mammography machine 12 to obtain a phantommammogram. As the composition of the phantom mammogram image is uniformand known, the intensity of the x-rays transmitted through the phantombreast 24 will vary based on the variation in the thickness of thephantom breast 24.

Referring to FIG. 3, there is illustrated in a perspective view, athree-dimensional triangular phantom 26 in accordance with an aspect ofthe invention. This triangular phantom 26 contains slabs of PMMA 26 a,as well as plastic layers 26 b and 26 c simulating 30% and 50%fibroglandular tissue respectively (from left to right—PMMA, 30%, 50%,PMMA). This three-dimensional triangular phantom 26 is then subjected toa mammogram to generate a set of image data. Again, this image data willvary only with the thickness of the triangular phantom 26. However, thethickness of the triangular phantom 26 will be known at any point. Thus,the set of image data for the triangular phantom 26 can be used tocorrelate the thicknesses of the triangular phantom 26, with particularpoints in the phantom mammogram having the same intensity of x-raytransmitted, and therefore being of the same thickness.

From the x-ray profile along the PMMA triangular phantom image from topseven centimeters to base less than one millimeter, the position alongthe wedge (i.e. the thickness) is determined from the logarithm of theimage pixel signal by interpolation using a second-degree polynomialfit. This fit is plotted as line 501 on the graph of FIG. 5. Thepolynomial function represented by line 501 of FIG. 5 allows directconversion from logarithmic gray pixel value to thickness value.

In a similar way, second-degree polynomial functions are found for 30%fibroglandular tissue and for 50% fibroglandular tissue. Thesecond-degree polynomial function for 30% fibroglandular tissue isplotted as line 503 in FIG. 5, and the second-degree polynomial functionfor 50% fibroglandular tissue is plotted as line 502 in FIG. 5. Asecond-degree polynomial function for 100% fibroglandular tissue wasobtained by mirroring the 30% polynomial function around the 50%polynomial function, and is represented as line 500 in FIG. 5. Anypercentage glandular composition can be verified by using slabs of knownthickness and composition.

The phantom thickness map 22 and polynomial functions 500, 501, 502 and503 can then be used to compute the thickness and density map of aparticular digital mammogram. First, this will require the phantomthickness map 22 to be rescaled to the size of the digital mammogram,and will require the thickness values of the phantom thickness map 22 tobe normalized to the thickness readout of the mammographic system. Next,the phantom thickness map is overlaid on a digital mammogram image usinga point-based elastic warping method, which is efficient at recoveringlocal deformations (see F. Bookstein, Thin-Plate Splines and theDecomposition of Deformations, IEEE Transactions Pattern Analysis andMachine Intelligence, 11, pp. 567-585, 1989). With this technique,special care is needed in the selection of landmarks. Two different setsof landmarks are chosen, both in the phantom thickness map 22 and in thedigital mammogram.

The phantom thickness object of FIG. 7 is defined and determined as theobject with thickness values larger than zero. Referring to FIG. 6,there is illustrated an intensity histogram 29 of a digital mammogram.This intensity histogram is bimodal. The breast thickness object 30 ofFIG. 8 is automatically generated from the histogram using a thresholdvalue 32 shown in FIG. 6. This threshold value 32 is at the middle pointof the valley between the two modes in the histogram. The boundaries ofboth the phantom thickness object of FIG. 7 and the breast thicknessobject of FIG. 8 are found by employing a morphological removingoperation. In the binary images of FIG. 7 and FIG. 8, a pixel is set tozero (black) if all of its four-connected neighbours are one (white),thus leaving only the boundary pixels on.

Having generated the phantom thickness object 22 of FIG. 7, and thebreast thickness object 30 of FIG. 8, it is possible to selectlandmarks. Referring to FIGS. 8 and 9 respectively, the phantomthickness object 22 and breast thickness object 30 are shown dividedinto segments. In the case of the phantom thickness object 22 of FIG. 9,these segments are defined by a series of radial lines 34 extending fromthe center 32 of the phantom thickness object 22 to the outer edge ofthe phantom thickness object 22. Each of these radial lines intersects afirst phantom boundary line 38 marking the outer edge of the phantomthickness object 22. Together, these intersection points provide a firstset of phantom landmarks 36. Similarly, in the case of the breastthickness object 30 of FIG. 10, the segments are defined by a series ofradial lines 44 extending from the center 42 of the breast thicknessobject 30 to the outer edge of the breast thickness object 30. Each ofthese radial lines intersects a first breast boundary line 48 markingthe outer edge of the breast thickness object 30. Together, theseintersection points provide a first set of breast landmarks 50.

Referring to FIG. 9, a second phantom boundary line inside the firstphantom boundary line is shown. This boundary line represents the pointat which the breast phantom 24 is no longer in contact with the breastcompression plate 18. This point is selected from a phantom thicknessprofile 60 of FIG. 11. Each of the radial lines 34 of FIG. 9 has anassociated thickness profile such as the thickness profile 60 of FIG.11. A line 62 is drawn connecting the first point 63 and last point 64of the thickness profile 60. A point 66 on the thickness profile 60 isthen selected to be a maximum distance from the line 62. This point 66is substantially at the point where the radial line 34 of the phantomceases being in contact with the breast compression plate 18. Together,the points 66 selected for all of the radial lines 34, generate thesecond boundary line 40.

A breast thickness profile 70 is plotted for each of the radial lines 44of the segmented breast thickness object 30 of FIG. 10. The logarithmicprofile values are converted to thickness using the polynomial functionfor 50% dense material. A thickness profile 70 of one such radial line44 is shown in FIG. 12. Unlike the thickness profile 60 of the breastphantom 24, the thickness of an actual breast is not uniform over afirst interval, but instead increases before decreasing. Similar to thecase of FIG. 11, a line 72 connecting the first point 73 on the profile70 with the last point 74 on the profile 70 is drawn. Then, a point 76is selected to be a maximum distance from the line 72. These points 76for all of the radial lines 44 are then plotted as points 52 on thesegmented breast thickness object 30 of FIG. 10, and are connected toprovide the second breast boundary line 46. Unlike the second phantomboundary line 40 of the phantom object of FIG. 9, the second boundaryline 46 of the breast thickness object of FIG. 10 is irregular,reflecting variation in the composition and compressibility of thebreast.

The minimum thickness values for thickness on the outer edge of thebreast thickness object are computed using the polynomial function for100% dense material, to convert logarithmical grey pixel values tothickness. The polynomial function for 100% dense material is selecteddue to the layer of skin surrounding the breast. A corrected warpedthickness map is then computed by cropping the radial lines 44 andcropping the map generally, at the minimum thickness value given by the100% conversion function. Next, the cropped profile is approximated by alinear combination of two exponentials using a non-linear least squareslogarithm.

Referring to FIGS. 13 and 14, there is illustrated in flowcharts amethod of generating a breast thickness map in accordance with an aspectof the present invention. In step 80 of the flowchart of FIG. 13, aphantom mammogram is obtained by imaging a breast phantom 24. Thisphantom mammogram contains a series of profiles of the breast phantomalong different planes, reflecting the difference in thickness of thebreast phantom at these different planes. The image data for differentthicknesses is then generated by imaging a three-dimensional triangularphantom 26. This triangular phantom contains slabs of PMMA, as well asplastics simulating 30 and 50% of fibroglandular tissue. By imaging thisthree-dimensional triangular phantom 26, image data for known anddifferent thicknesses are generated. This information can then becombined with the information provided by step 80, to determine aphantom thickness map object 22 in step 84. Then, in steps 86 and 88, afirst set of phantom landmarks, and a second set of phantom landmarksare determined.

Referring to FIG. 14, a digital mammogram of an actual breast isobtained in step 90. Then, in steps 92 and 94 respectively, a first setof breast landmarks, and a second set of breast landmarks are defined.In step 96, the phantom thickness map is rescaled to the size of thedigital mammogram, and in step 98, the phantom thickness map object isnormalized by normalizing its thickness size to the thickness readout ofthe mammography system. In step 100, the phantom thickness map object isoverlaid on the digital mammogram using a point-based elastic warpingmethod, which is efficient at recovering local deformations.

Referring to FIG. 15, there is illustrated in a flowchart a method ofselecting a first set of phantom landmarks and a second set of phantomlandmarks in accordance with an aspect of the present invention. In step110, a series of radial lines extending from the center of the phantomthickness object 22 to its outer edge are generated. In step 112, afirst set of phantom landmarks are determined by taking the intersectionof these radial lines with the outer edge of the phantom thicknessobject. Then, in step 114, a secondary boundary of the phantom thicknessobject 22 is determined. This secondary boundary of the phantomthickness object is defined by the points at which the phantom thicknessobject moves from being in contact with the breast compression plate, tonot being in contact with the breast compression plate. Then, in step116, a second set of phantom landmarks is determined. This second set ofphantom landmarks is determined by taking the intersection of the radiallines generated in step 110 with the secondary boundary generated instep 114.

Referring to FIG. 16, there is illustrated in a flowchart a method ofselecting a first set of breast landmarks and a second set of breastlandmarks in accordance with an aspect of the present invention. In step120, a series of radial lines extending from the center of the breastimage to its outer edge are generated. In step 122, a first set ofbreast landmarks are determined by taking the intersection of theseradial lines with the outer edge of the breast image. Then, in step 124,a secondary boundary of the breast image is determined. This secondaryboundary of the breast image is defined by the points at which thebreast changes from being in contact with the breast compression plate,to not being in contact with the breast compression plate. Then, in step126, a second set of breast landmarks is determined. This second set ofbreast landmarks is determined by taking the intersection of the radiallines generated in step 120 with the secondary boundary generated instep 124.

According to a preferred aspect of the present invention, step 100 ofthe flowchart of FIG. 14 is executed by applying the point-based elasticwarping method to warp the first set of phantom landmarks into the firstset of breast landmarks, and to warp the second set of phantom landmarksinto the second set of breast landmarks.

Other variations and modifications of the invention are possible. Forexample, phantom thickness objects may be generated in other ways by,say, for example, assembling an average breast from a series ofmammograms for different women, or by selecting a stored breastthickness object that most closely matches the shape and dimensions ofthe breast being imaged from a library of previously obtained breastthickness objects. Further, other techniques may be applied to overlaythe phantom thickness map on the breast thickness object. All suchmodifications or variations are believed to be within the sphere andscope of the invention as defined by the claims appended hereto.

1. A method of generating a three-dimensional breast thickness objectfor a digital mammogram of a breast, the method comprising: (a)generating a phantom thickness object for transforming into the breastthickness object, the phantom thickness object being generated in athree-dimensional modeling means and being substantially breast-shaped;(b) determining a set of dimensions for the breast; and (c) transformingthe phantom thickness object to conform to the set of dimensions toprovide the three-dimensional breast thickness object in thethree-dimensional modeling means.
 2. The method as defined in claim 1wherein the set of dimensions comprises a thickness readout for thebreast and a size of the digital mammogram and wherein step (c)comprises normalizing a set of thickness values of the phantom thicknessobject based on the thickness readout for the breast; and, rescaling thephantom thickness object to the size of the digital mammogram.
 3. Themethod as defined in claim 2 further comprising determining a set ofphantom landmarks at the edge of the phantom thickness object;determining a set of breast landmarks at the edge of the digitalmammogram; and warping the phantom thickness object to map the set ofphantom landmarks onto the set of breast landmarks.
 4. The method asdefined in claim 3 further comprising determining a second set ofphantom landmarks on the phantom thickness object; estimating a breastdensity at a second set of points in the digital mammogram to determinea breast local thickness at the second set of point and a second set ofbreast landmarks corresponding to the second set of points; and warpingthe phantom thickness object to map the second set, of phantom landmarksonto the second set of breast landmarks.
 5. A computer program productfor use on a computer system for analyzing digital mammograms, thecomputer program product comprising (a) a recording medium; (b) phantomthickness object generation means recorded on the recording medium forinstructing the computer system to generate the phantom thicknessobject; (c) data entry generation means recorded on the recording mediumfor instructing the computer system to upload a set of dimensions forthe breast; and, (d) transformation generation means recorded on therecording medium for instructing the computer system to transform thephantom thickness object to conform to the set of dimensions for thebreast to provide the three-dimensional breast thickness object.
 6. Thecomputer program product as defined in claim 5 wherein the set ofdimensions comprises a thickness readout for the breast and a size ofthe digital mammogram, and wherein the transformation generation meanscomprises normalizing means for instructing the computer system tonormalize a set of thickness values of the phantom thickness objectbased on the thickness readout of the breast; rescaling means forinstructing the computer system to rescale the phantom thickness objectto the size of the digital mammogram.
 7. The computer program product asdefined in claim 6 further comprising first phantom landmark generationmeans recorded on the recording medium for instructing the computersystem to determine a set of phantom landmarks at the edge of thephantom thickness object; and first breast landmark generation meansrecorded on the recording medium for instructing the computer system todetermine a set of breast landmarks at the edge of the digitalmammogram; wherein the transformation generation means is operable toinstruct the computer system to warp the phantom thickness object to mapthe set of phantom landmarks onto the set of breast landmarks.
 8. Thecomputer program product as defined in claim 7 further comprising secondphantom landmark generation means recorded on the recording medium forinstructing the computer system to determine a second set of phantomlandmarks at the edge of the phantom thickness object; and second breastlandmark generation means recorded on the recording medium forinstructing the computer system to estimate a breast density at a secondset of points in the digital mammogram to determine a breast localthickness at the second set of point and a second set of breastlandmarks corresponding to the second set of points; wherein thetransformation generation means is operable to instruct the computersystem to warp the phantom thickness object to map the second set ofphantom landmarks onto the second set of breast landmarks.
 9. A computersystem for analyzing digital mammograms, the computer system comprising(a) phantom thickness object generation means for generating the phantomthickness object; (b) data entry means for receiving a set of dimensionsfor a breast; and, (c) transformation means for transforming the phantomthickness object to conform to the set of dimensions for the breast toprovide the three-dimensional breast thickness object.
 10. The computersystem as defined in claim 9 wherein the set of dimensions comprises athickness readout for the breast and a size of the digital mammogram,and wherein the transformation means comprises normalizing means fornormalizing a set of thickness values of the phantom thickness objectbased on the thickness readout of the breast; and, rescaling means forresealing the phantom thickness object to the size of the digitalmammogram.
 11. The computer system as defined in claim 10 furthercomprising first phantom landmark determining means for determining aset of phantom landmarks at the edge of the phantom thickness object;and first breast landmark determining means for determining a set ofbreast landmarks at the edge of the digital mammogram; wherein thetransformation means is operable to warp the phantom thickness object tomap the set of phantom landmarks onto the set of breast landmarks. 12.The computer system as defined in claim 11 further comprising secondphantom landmark determining means for determining a second set ofphantom landmarks at the edge of the phantom thickness object; andsecond breast landmark generation determining means for estimating abreast density at a second set of points in the digital mammogram todetermine a breast local thickness at the second set of point and asecond set of breast landmarks corresponding to the second set ofpoints; wherein the transformation means is operable to warp the phantomthickness object to map the second set of phantom landmarks onto thesecond set of breast landmarks.